Unit definitions

Spat

One full sphere equals one spat. Therefore, a spat equals $4\pi\ \text{sr}$.

Steradian

The steradian is the SI unit of solid angle. If you take a sphere and mark an area on its surface that has a surface area of $r^2$, where $r$ is the radius of the sphere, then the solid angle formed at the center is $1\ \text{sr}$.

How to convert Spat to Steradian

$$\text{Solid Angle}_{\text{sr}} = \text{Solid Angle}_{\text{sp}} \cdot 4 \cdot 3.141592653589793$$

Examples

Example 1

Convert $35.0\ \text{sp}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 35.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 439.822972$$

$$\therefore \ 35.0\ \text{sp} = 439.822972 \ \text{sr}$$

Example 2

Convert $65.0\ \text{sp}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 65.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 816.81409$$

$$\therefore \ 65.0\ \text{sp} = 816.81409 \ \text{sr}$$

Example 3

Convert $120.0\ \text{sp}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 120.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 1507.964474$$

$$\therefore \ 120.0\ \text{sp} = 1507.964474 \ \text{sr}$$

Example 4

Convert $140.0\ \text{sp}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 140.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 1759.291886$$

$$\therefore \ 140.0\ \text{sp} = 1759.291886 \ \text{sr}$$

Example 5

Convert $160.0\ \text{sp}$ to $\text{sr}$.

$$\text{Solid Angle}_{\text{sr}} = 160.0 \cdot 4 \cdot 3.141592653589793$$

$$\text{Solid Angle}_{\text{sr}} = 2010.619298$$

$$\therefore \ 160.0\ \text{sp} = 2010.619298 \ \text{sr}$$

Spat to Steradian conversion table

Spat to Steradian conversion table

Spat [sp]	Steradian [sr]
1	12.566371
2	25.132741
3	37.699112
4	50.265482
5	62.831853
6	75.398224
7	87.964594
8	100.530965
9	113.097336
10	125.663706

Convert Spat to other Solid Angle units

Convert Spat to other Solid Angle units

Spat [sp]	Other unit
1	1 Full sphere [4π sr]